Answer
$A=k\sqrt{xy}$
where k = constant of proportionality
Work Step by Step
RECALL:
If the quantities (or variables) $x, y$ and $z$ are related by the equation $y=kxz$, then $y$ is jointly proportional to $x$ and $y$, where $k$ is the constant of proportionality.
$A$ is given to be jointly proportional to $\sqrt{x}$ and $\sqrt{y}$ therefore the equation that expresses the given statement is:
$A = k(\sqrt{x} \sqrt{y})$
where k = constant of proportionality